Heat butter and oil in a multi-functional pressure cooker (such as Instant Pot) set to Saute function. Add chicken to the hot pot; stir in garlic and oregano. Cook and stir until chicken is golden brown, 5 to 7 minutes.
Pour chicken broth into the pot and bring to a boil while scraping the browned bits of food off the bottom of the pan with a wooden spoon. Stir in pasta and whipping cream. Add spinach and sun-dried tomatoes on top. Hit Cancel.
Close and lock the lid. Select high pressure according to manufacturer's instructions; set timer for 10 minutes. Allow 10 to 15 minutes for pressure to build.
Release pressure using the natural-release method according to manufacturer's instructions, about 15 minutes; quick-release remaining pressure. Unlock and remove the lid.
Stir in 1 cup Parmesan cheese until melted. Top with soffrito seasoning and extra cheese if desired. Serve immediately.